CHE $1300$

Homework #$3$

I am designing the waste water treatment center for Earle Hall. The labs use a lot of acetone for cleaning glassware, which has to be removed from the water before it is sent to the city for further processing. I want to produce one stream that is high$-$purity acetone, that will be recycled back to Earle Hall so that the labs can re$-$use it$.$ Assume that the stream leaving Earle Hall is $250,000$ lbm every day, and the stream is $5$ mass $\%$ acetone in water. I put this stream into a steady$-$state separator, which creates one stream which is $95$ mass$\%$ acetone $($and is recycled to Earle Hall for use$),$ and one stream which is $1$mass$\%$ acetone $($and is sent to the city's sewer system$).$ What will be the flowrate of the stream to the city sewer?

I sent the preliminary design for the new waste water treatment center described above to the city, and someone did a quick calculation which showed that a lot of acetone would be going into the city sewer. They didn't like the sound of that. So they asked me to re$-$design the separator, this time, with the added constraint that there be no more than $100lbm$ per day of Acetone in the stream that gets sent to the city sewer. Assume that the stream leaving Earle Hall is still $250,000$ lbm every day, and the stream is still $5$ mass $\%$ acetone in water. Also, assume that the stream created to recycle acetone to Earle Hall will still have a composition that is $95$ mass $\%$ acetone. What will the flowrate of the Recycle stream be$,$ and what will be the mass $\%$ of acetone in the of the stream sent to the city sewer?

I sent the re$-$design back to the city, but I complained that the separator they wanted was going to cost a lot of money and energy. So they sent me more requirements; in truth, I$\text{'}$m not sure that the new requirements help me$,$ or hurt me$!$ They added the requirement that my recycle stream contain $99\%$ of the acetone that was fed to my separator, and that the system maintains the $1$mass$\%$ acetone in the stream sent to the city's sewer system. Assume that the stream leaving Earle Hall is still $250,000$ lbm every day, and is still $5$ mass $\%$ acetone in water. What will the flowrate to the city's sewer system be$,$ and what will be the mass $\%$ of acetone in the stream I recycle to Earle Hall $($i$.$e$.,$ it won't still be $95\%$ like I wanted$)?$

Well, that design isn't going to work, either. I think about the only thing I can do is to try to change the concentration of the stream that is leaving Earle Hall. I need my recycle stream to contain $99\%$ of the acetone that leaves Earle, and have a mass $\%$ of acetone of $95\%($or else I can't reuse it$),$ and I need the stream that is sent to the city's sewer to have $1$mass$\%$ acetone. What is the mass $\%$ of acetone in the stream leaving Earle that makes this possible? Assume that the stream leaving Earle Hall is still $250,000$ lbm every day.